1. Field of the Invention
The present invention relates to a sensor using a ring resonator, and more particularly, it relates to a method of reducing the polarization fluctuation inducing drift in a resonator fiber optic gyro to measure the differential resonant frequency generated by the rotation between two light waves facing each other propagating in the ring resonator.
2. Description of the Related Art
Fiber optic gyros (FOG: Fiber Optic Gyro) to detect the rotational speed of an object for measurement making use of the Sagnac Effect generated by the rotation include a resonator fiber optic gyro (R-FOG: Resonator Fiber Optic Gyro). The R-FOG can obtain the high sensitivity by the short fiber length making use of the sharp resonance characteristic of the ring resonator.
The ring resonator will be described below.
The R-FOG uses a reflector ring resonator or a transmitter ring resonator comprising an optical fiber and a coupler as a sensing loop. The reflector ring resonator comprises a sensing loop 33 and a coupler 32 as shown in FIG. 9(a). The resonance characteristic shown in FIG. 10(a) can be obtained when the laser beam is incident from a port 1 and the intensity of the emitted light is observed at a port 2 to acquire the characteristic of the incident light to the frequency. The transmitter ring resonator comprises a sensing loop 36 and two couplers 35 and 37 as shown in FIG. 9(b). The resonance characteristic shown in FIG. 10B can be obtained when the laser beam is incident from the port 1 and the intensity of the emitted light is observed at the port 2. The space of the resonance points is referred to as the free spectrum range, and given as follows:                               ν          FSR                =                  c          nL                                    (        1        )            
where c is the velocity of light, n is the refractive index of the optical fiber, and L is the sensing loop length.
The fineness is the parameter showing the sharpness of the resonance, and defined by the formula (2).                     F        =                                            ν              FSR                        Δν                    =                                    π              ⁢                                                α                  ⁢                                      xe2x80x83                                    ⁢                  R                                                                    1              -                              α                ⁢                                  xe2x80x83                                ⁢                R                                                                        (        2        )            
where xcex94v is the full width at half maximum of the resonance characteristic shown in FIG. 10, R is the branching ratio of the coupler, and xcex1 is the loss in the ring resonator. Generally speaking, the detection sensitivity as the gyro is increased as the fineness is increased.
The resonance characteristic can also be obtained similarly by setting the X-axis as the phase difference between two light waves different by one trip propagating around the ring resonator as shown in FIG. 11. The space of the resonance points adjacent to each other is just 2xcfx80.
The principle of detecting the rotation of the R-FOG is that, when the ring resonator is rotated at the angular velocity xcexa9, an optical path difference is generated due to Sagnac Effect in the optical path length of the clockwise light wave (CW light) and the counterclockwise light wave (CCW light), and the difference is generated thereby in the resonant frequency of the CW light and the CCW light. The difference in resonant frequency is expressed as follows:                               Δν          s                =                                            4              ⁢              S                                      λ              ⁢                              xe2x80x83                            ⁢              L                                ⁢          Ω                                    (        3        )            
where S is the area surrounded by the ring resonator, and xcex is the wavelength of the oscillated laser beam. The angular velocity xcexa9 is obtained by measuring the difference in the resonant frequency.
FIGS. 12 and 13 show the general configuration of the R-FOGs using the reflector ring resonator and the transmitter ring resonator, respectively.
The light emitted from laser beam sources 41 and 49 is branched into two by a beam splitter BS. The two branched lights pass through lenses L1 and L2, respectively, and are guided to the optical fiber, and incident in a coupler C1. The lights incident in ring resonators 46 and 54 by the coupler C1 propagate in the loop clockwise (CW) and counterclockwise (CCW).
The resonance characteristic is observed by a light receiver D1 for the CW light and by a light receiver D2 for the CCW light, respectively. In order to detect the resonance point, both the CW light and the CCW light are bias-modulated by the sinusoidal wave having the frequency fn and the frequency fm by phase modulators PM2 and PM1 before the lights are incident in the ring resonators 46 and 54. The frequency fn and the frequency fm are generated by oscillators (1) 44 and 53 and oscillators (2) 45 and 52. The differential resonance characteristic can be obtained through the synchronous detection at the frequency of the sinusoidal wave. The resonance point is the frequency of the light wave at which the differential resonance characteristic is zero, and can be detected and traced through the feedback thereto.
In the R-FOG, the reciprocal effect to the CW light and the CCW light is separated from the non-reciprocal effect due to Sagnac Effect.
Generally, for the reciprocal effect, a method for feedback to the frequency of oscillation of the laser beam source based on the output of the light receiver of either the CW light or the CCW light is employed in order to follow the resonance point to be shifted.
The method for bias modulation to detect the resonance point is possible by implementing the binary frequency shift by the xe2x80x9cdigital serrodynexe2x80x9d at a predetermined switching frequency as introduced in Kazuo Hotate and Michiko Harumoto, xe2x80x9cRESONATOR FIBER OPTIC GYRO USING DIGITAL SERRODYNE MODULATIONxe2x80x9d, IEEE J. Lightwave Technol., Vol. 15, No. 3, pp. 466-473, 1997 (Literature 1).
In FIGS. 12 and 13, the CW light and the CCW light are synchronously detected by a synchronous detection circuit LIA1 and a synchronous detection circuit LIA2, respectively, and the deviation in the resonant frequency can be detected. The output of the synchronous detection circuit LIA1 is inputted in laser frequency control circuits 39 and 47, and control device so that the laser beam frequency f0 agrees with one resonance point with reference to the CW light. The output of the synchronous detection circuit LIA2 is obtained from the deviation in the resonance point between the CW light and the CCW light as the voltage value. This is the open loop output of the gyro.
In order to expand the range of detection, a closed loop system using the serrodyne (sawtooth) wave is used. The serrodyne wave works to change the frequency of the light wave by the frequency of the serrodyne wave with the amplitude thereof as the voltage value to give the phase rotation of 2xcfx80. An electro-optic modulator formed on a lithium niobate (LiNbO3:LN) waveguide is extensive in frequency range, and used in modulation by the serrodyne wave.
The output of the synchronous detection circuit LIA2 is inputted in integrators 43 and 51 for integration control, and the output of the integrators is inputted in a voltage control oscillator VCO to change the frequency f2 of the serrodyne wave generated by a serrodyne wave generator. The serrodyne wave is inputted in a waveguide type phase modulator LN2, and controlled so that the CCW light agrees with the resonance point. The frequency of the CCW light becomes f0+f2. The closed loop output of the gyro can be obtained by counting the frequency f2 of the serrodyne wave.
In order to further improve the resolution, the serrodyne wave having a fixed frequency f1 is inputted in the CW light using a waveguide type phase modulator LN1 simultaneously with the input of the serrodyne wave in the CCW light. The frequency of the CW light in this condition becomes f0+f1. As a result, the difference in the frequency f2xe2x88x92f1 between the CCW light and the CW light becomes the closed loop output of the gyro.
Polarization fluctuation which is one of the error factors of the R-FOG will be described below.
The polarization fluctuation means the change of the polarization condition of the light wave by the unevenness of the waveguide or the polarization dependency, and is considerably affected by the environmental conditions including the temperature or the like.
Thus, a polarization maintaining fiber (PMF: Polarization Maintaining Fiber) is generally used. The polarization maintaining fiber has two axes of polarization along which the linearly polarized wave can be propagated.
However, even when the polarization maintaining fiber is used, it is practically impossible to selectively use one axis of polarization due to the crosstalk of the optical fiber (the waveguide) and the coupler, and the assembly errors in manufacturing the ring resonator, and the resonance characteristic of the ring resonator has the characteristic of superposing two eigenstates of polarization (ESOP: Eigenstate of Polarization). The Eigenstate of Polarization (ESOP) means the polarization condition that the light wave is not changed when the light wave makes one trip around the ring resonator, and corresponds to two eigenvectors of the transfer matrix expressing one trip of the ring resonator.
Next, the condition that two ESOPs affect the gyro output will be described below.
More correctly, in the ring resonator shown in FIG. 9, at least one splice (fusion) point is required in the sensing loop as shown in FIG. 14. The fusion angle xcex8 must be adjusted here so that the axes of polarization of fibers for fusion must agree with each other; however, the rotation of the axes of polarization is generated due to the angular deviation. In addition, the crosstalk at the sensing loop and the polarization coupling at the coupler or the lead part are generated. Thus, even when the laser beam of the linearly polarized wave is incident only on X-axis, the light wave is actually coupled with Y-axis in an unwanted manner, appearing an aspect different from an ideal one.
In the resonance characteristic observed by the light receiver, the resonance points corresponding to two ESOPs appear as shown in FIG. 15. When ESOP having the resonance point used to detect the rotation is defined as ESOP1, ESOP2 has an unwanted resonance point. The positional relationship of the resonance points of ESOP1 and ESOP2 is dependent on the length of the resonator, i.e., the length of the sensing loop, and fluctuated according to the environmental temperature, etc. The resonance point of ESOP2 is increased as the distance from ESOP1 is decreased. FIG. 15 shows this condition in a part expressed by chain lines.
Approach of the resonance point of ESOP2 to the resonance point of ESOP1, and duplication thereof lead to a very large error factor of the gyro output, which is quantitatively verified in K. Takiguchi and K. Hotate, xe2x80x9cBIAS OF AN OPTICAL PASSIVE RING-RESONATOR GYRO CAUSED BY THE MISALIGNMENT OF THE POLARIZATION AXIS IN THE POLARIZATION-MAINTAINING FIBER RESONATORxe2x80x9d, IEEE J. Lightwave Technol., Vol. 10, No. 4, pp. 514-522, 1992 (Literature 2). According to the literature, the resonance points of two ESOPs are duplicated when xcex94xcex2L which is the product of the difference AP in the propagation constant of two axes of polarization of the polarization maintaining fiber used in the ring resonator and the length L of the sensing loop fiber is xcex94xcex2L=2 mxcfx80 (m: integer), and the resonance points of two ESOPs are separated most from each other when xcex94xcex2L=xcfx80+2mxcfx80 (m: integer), and the unwanted resonance points of ESOP2 can be minimized.
However, xcex94xcex2L is changed by at least xcfx80 in the temperature change of about 1xc2x0 C., and in reality, duplication of the resonance points cannot be avoided. In order to solve this problem, the fusion is implemented with the axes of polarization of the polarization maintaining fiber twisted by 90xc2x0 at the splice point in the ring resonator as shown in FIG. 16 (xcex8=90xc2x0), and this method has been disclosed in U.S. Pat. No. 5,018,857, Sanders et al., xe2x80x9cPASSIVE RESONATOR GYRO WITH POLARIZATION ROTATING RING PATHxe2x80x9d (Literature 3) and Sanders et al., xe2x80x9cNOVEL POLARIZATION-ROTATING FIBER RESONATOR FOR ROTATION SENSING APPLICATIONSxe2x80x9d, Proc. SPIE, Fiber Optic and Laser Sensors VII., Vol. 1169, pp. 373-381, 1989 (Literature 4).
The rotation of 90xc2x0 of the polarized wave in the ring resonator equally excites two ESOPs as shown in FIG. 17, and since the resonance point of one ESOP is located at the center of the other resonance point which repeatedly appears, and the resonance points of the two ESOPs do not duplicate even when the length of the resonator is changed.
In addition, if the angular deviation at the 90xc2x0 splice point is 1xc2x0 (xcex8=89xc2x0 or xcex8=91xc2x0), and the fineness of the resonator is not less than 100, it has been analyzed that the error is not more than 10xe2x88x927 (radian/s) which is the accuracy required for the inertial navigation of an aircraft in K. Takiguchi and K. Hotate, xe2x80x9cEVALUATION OF THE OUTPUT ERROR IN AN OPTICAL PASSIVE RING-RESONATORxe2x80x9d, IEEE Photon. Technol., Vol. 3, No. 1, pp. 80-90, 1991 (Literature 5). However, it is assumed in this analysis that no polarization dependency is present in the ring resonator.
However, the experimental result that the polarization dependency which has been assumed to be absent works as a large error factor, and the performance expected from the theoretical analysis cannot be achieved, is demonstrated in L. K. Strandjord and G. A. Sanders, xe2x80x9cRESONATOR FIBER OPTIC GYRO EMPLOYING A PORARIZATION-ROTATING RESONATORxe2x80x9d, Proc. SPIE, Vol. 1585, Fiber Optic Gyros: 15th Anniversary Conference, 1991 (Literature 6).
In order to clarify the problems, the analysis shown in Literature 5 will be described. This analytical method is theoretically developed in detail by Literature 2, and the models used in the analysis are substantially equivalent to each other. The main difference is that the angle xcex8 at the splice point is set to be xcex8≈0xc2x0 in the latter analysis, while xcex8 is set to be xcex8≈90xc2x0 in the former analysis.
FIG. 18 shows a model of the ring resonator used in these analyses. P1 and P2 are polarizers connected to the lead part of the ring resonator. However, in the analysis of the 90xc2x0 splice (Literature 5), no polarizer is inserted in the lead part of the ring resonator. The coupler is assumed to be free from any polarization dependency in both analyses. E0CW and E0CCW in FIG. 18 are the laser beam incident in the ring resonator, where the incident light is assumed to be the linearly polarized wave, and xcex8iCW and xcex8iCCW express the angular deviation to the axes of polarization of the fiber. L means the length of the fiber of the sensing loop, and L1 and L2 mean the lengths of two portions divided from the coupler 55 at the splice point. xcex94L is the difference therebetween.
According to Literature 2, the power, i.e., the resonance characteristic of one light to be observed by the light receiver is summarized in the following form:
|EdCW/E0CW|2=K1|U1|2+K2|U2|2+K3xe2x80x83xe2x80x83(4) 
where             "LeftBracketingBar"              U        j            "RightBracketingBar"        2    =            K      4        ⁡          [              1        -                              K            5                                                              (                                  1                  -                                      K                    6                                          1                      /                      2                                                                      )                            2                        +                          4              ⁢                              K                6                                  1                  /                  2                                            ⁢                                                sin                  2                                ⁢                                  (                                                            β                      j                                        ⁢                                          L                      /                      2                                                        )                                                                        ]      
The resonance characteristic for the CCW light is similar thereto.
In the formula, Ki (i=1 to 6) is the constant determined by the parameters of the ring resonator, and xcex2j (j=1, 2) is the propagation constant of each ESOP. First, second and third terms in the formula (4) mean the interference components expressed by ESOP1, ESOP2 and the product thereof. The third term is generated only when the factor of the polarization dependency is present in the ring resonator and in the lead part to the light receiver.
The differential resonance characteristic obtained by differentiating the formula (4) is required to detect the resonance point.
The differential resonance characteristic is controlled to be zero by the closed loop system. The resonance point of ESOP1 is used here to detect the rotation. The differential resonance characteristic is decomposed into three components corresponding to ESOP1, ESOP2 and the interference component as shown in FIG. 19, and the operation point of the resonance point of ESOP1, i.e., the position at which the differential resonance characteristic is zero is deviated from "xgr"=2qxcfx80 (q:integer) due to the presence of ESOP2 and the interference component. In order to calculate the operation point, the formula (4) is differentiated by the phase corresponding to each term to obtain "xgr" to satisfy the formula (5).
D1("xgr")+D2("xgr"xe2x88x92xcex94xcex2xe2x80x2)+D3("xgr", "xgr"xe2x88x92xcex94xcex2xe2x80x2)=0xe2x80x83xe2x80x83(5) 
Di (i=1 to 3) expresses the differentiation by "xgr" of the i-th term in the formula (4), and xcex94xcex2xe2x80x2 is the difference in the propagation constant between two ESOPs. With N as an integer, the deviation from "xgr"=2qxcfx80 (q:integer) converted in the angular velocity is expressed as follows:                     ΔΩ        =                                                            c                0                            ⁢              λ                                      4              ⁢              π              ⁢                              xe2x80x83                            ⁢              Lr                                ⁢                      (                          ζ              -                              2                ⁢                N                ⁢                                  xe2x80x83                                ⁢                π                                      )                                              (        6        )            
where c0, xcex and r are the velocity of light in vacuum, the wavelength of the light source, and the radius of the ring resonator, respectively.
Since the difference at each operation point of the CW light and the CCW light is used for the output to detect the rotation, the operations of the formulae (4) to (6) are implemented for the CW light and the CCW light, respectively, and the difference is defined as the error of the gyro output.
As described above, in the analysis of the 90xc2x0 splice, no polarizer is inserted in the lead part of the ring resonator.
The transfer matrix of the polarizer is expressed as follows:                               P          1                =                              (                                                            1                                                  0                                                                              0                                                                      ϵ                    i                                                                        )                    ⁢                      (                                          i                =                1                            ,              2                        )                                              (        7        )            
The polarization dependency loss is similarly expressed.
Thus, xcex51=xcex52=1, and the third term in the formula (4) is not generated. Thus, the calculated error is affected only by ESOP2.
However, it is impossible that the polarization dependency loss is completely not present. The effect can be checked by substituting the numerical value such as 0.9999 which is slightly changed from 1 into xcex51 (i=1, 2).
FIG. 20 shows the errors of the gyro output calculated by substituting 1, 0.9999, 0.999 and 0.99 in xcex51.
It is understood from FIG. 20 that the errors of the gyro output are rapidly increased by the slight change in xcex51. It is thus understood that the calculated error with xcex5i=1 for a condition in which no polarizer is used, i.e., the accuracy of the gyro cannot be expected in practice.
Separate from the present invention, the countermeasures have been tried for the above problems, and disclosed in U.S. Pat. No. 5,296,912, Strandjord et al., xe2x80x9cR-FOG ROTATION RATE ERROR REDUCER HAVING RESONATOR MODE SYMMETRIZATIONxe2x80x9d (Literature 7) and L. K. Strandjord and G. A. Sanders, xe2x80x9cPERFORMANCE IMPROVEMENTS OF A POLARIZATION-ROTATING RESONATOR FIBER OPTIC GYROSCOPExe2x80x9d, Proc. SPIE, Fiber Optic and Laser Sensors X, Vol. 1795, pp. 94-104, 1992 (Literature 8).
In the countermeasures, the error can be reduced if the frequency is switched to allow the frequency of oscillation of the light source to alternately follow ESOP1 and ESOP2, and the output generated in each case is averaged by using the different sign of the error when ESOP1 is used for detecting the rotation, and when ESOP2 is used for detecting the rotation.
In addition, the countermeasures that the output of the ring resonator observed by the light receiver has no errors is disclosed in L. Strandjord and G. Sanders, xe2x80x9cPASSIVE STABILIZATION OF TEMPERATURE DEPENDENT POLARIZATION ERRORS OF A POLARIZATION-ROTATING RESONATOR FIBER OPTIC GYROSCOPExe2x80x9d, Proc. SPIE, Fiber Optic and Laser Sensors XIII, Vol. 2510, pp. 81-91, 1995 (Literature 9). The countermeasures were verified for the transmitter ring resonator.
In this countermeasures, the error is reduced if the difference between the length L1 from the first coupler to the 90xc2x0 splice point and the length L2 from the second coupler and the 90xc2x0 splice point is zero, and the length L3 between the first coupler and the second coupler is close to zero, where L1, L2 and L3 are the lengths of three portions of the optical fiber divided by the first coupler in which the light wave emitted from the laser beam source first reaches, the 90xc2x0 splice point in the ring resonator, and the second coupler to emit the light wave and input the light wave in the light receiver, respectively.
However, in the theoretical development leading to the result, a large number of approximations are used, and a focus is placed in the space between the resonance point of ESOP1 and the resonance point of ESOP2, i.e., in that one resonance point is located in the center of the other repeatedly appearing resonance point; however, the mechanism of generation of the error appearing in the gyro output is not analyzed.
The present invention has been made to solve various problems described above, and an object of the present invention is therefore to provide a method of eliminating the error generated in the output of a resonator fiber optic gyro even when the loss in the polarization dependency which has never been solved in conventional methods is present in a ring resonator.
A method of reducing the polarization fluctuation inducing drift in a resonator fiber optic gyro includes the step of setting xcex94L so that the relationship of xcex94L and xcex94xcex2 satisfies a formula xcex94xcex2xcex94L=xcfx80+2nxcfx80 [radian] (n: integer), or approximately satisfies the formula to minimize the error induced by the polarization fluctuation where xcex94L is the difference in length between L1 and L2 of two portions of a waveguide divided by a coupler and the polarization-rotating point, and xcex94xcex2 is the difference in propagation constant of two axes of polarization of the waveguide in a method of measuring the non-reciprocal effect such as the rotation in a reflector ring resonator comprising a sensing loop formed of the waveguide having two axes of polarization to propagate the light wave, and the coupler which is inserted in said sensing loop, guides the light wave from a laser beam source to said sensing loop and emits the light wave in said sensing loop, and having a polarization-rotating point in said sensing loop.
The method of reducing the polarization fluctuation inducing drift in a resonator fiber optic gyro includes the step of setting xcex94L and L3 so that the relationship of xcex94L, xcex94xcex2 and L3 satisfies a formula xcex94xcex2xcex94L=xcfx80+2nxcfx80 [radian] (n: integer) and xcex94xcex2L3=m xcfx80 [radian] (m: integer), or approximately satisfies the formulae to minimize the error induced by the polarization fluctuation where L1 is the distance from said first coupler to the polarization-rotating point, L2 is the distance from the polarization-rotating point to said second coupler, L3 is the distance from said second coupler to said first coupler, xcex94L is the difference between L1 and the length (L2+L3) from the polarization-rotating point to said first coupler through said second coupler, and xcex94xcex2 is the difference in propagation constant of two axes of polarization of the waveguide when the waveguide is divided into three portions by said first coupler, said polarization-rotating point and said second coupler in a method of measuring the non-reciprocal effect such as the rotation in a transmitter ring resonator comprising a sensing loop formed of the waveguide having two axes of polarization to propagate the light wave, a first coupler to guide the light wave from a laser beam source to said sensing loop and a second coupler to emit the light wave in said sensing loop which are inserted in said sensing loop, and having a polarization-rotating point in said sensing loop.
In the present invention, the polarization-rotating angle at the polarization-rotating point can be set to be about 90xc2x0 in the above configuration.
The method of reducing the polarization fluctuation inducing drift in a resonator fiber optic gyro includes the step of minimizing the error irrespective of any change in xcex94xcex2L by controlling xcex94L making use of the fact that the characteristic of said measurement error is considerably dependent on the product of xcex94xcex2 and xcex94L where xcex94L is the difference in length of two portions of a waveguide divided by said first coupler and said polarization-rotating point, and xcex94xcex2 is the difference in propagation constant of two axes of polarization of the waveguide, and less dependent on xcex94xcex2L which is the product of the sum of the length of two portions of the waveguide (L) and xcex94xcex2 which is the sum in propagation constant of two axes of polarization of the waveguide in a method of measuring the non-reciprocal effect such as the rotation in a reflector ring resonator or a transmitter ring resonator comprising a sensing loop formed of the waveguide having two axes of polarization to propagate the light wave and a coupler inserted in said sensing loop, and having a polarization-rotating point in said sensing loop.
In the present invention, the error is minimized irrespective of any change in xcex94xcex2L through the feedback to the difference xcex94L in length between two portions of a waveguide divided by a coupler in which the light wave emitted from a laser beam source reaches first and the polarization-rotating point in a ring resonator making use of generation of an error signal indicating the deviation from an optimum value of xcex94xcex2xcex94L at a predetermined period by alternately applying two different depths of modulation in the bias modulation implemented for detecting a resonance point at the predetermined period.
In the above configuration, the ring resonator itself can be set in a condition in which no errors are generated even when the polarization dependency loss is present in the ring resonator. Thus, the resonator fiber optic gyro using this method can suppress the errors of the gyro output induced by the polarization fluctuation to a minimum, and reduce the drift of the gyro output caused by the change in the errors. The gyro high in accuracy can thus be realized.